Fig. 1

Selection of the optimal λ value for variable selection using Lasso regression (left) and coefficient shrinkage paths of predictors (right). The left panel displays the binomial deviance for different log(λ) values, where red dots represent the mean deviance, and the error bars indicate standard deviations. Two vertical dashed lines correspond to the λ values selected by the minimum mean squared error criterion (left line) and the one-standard-error rule (right line), respectively. The right panel illustrates the coefficient shrinkage paths of different predictors as log(λ) changes, with each line representing a variable. As λ increases, coefficients gradually shrink toward zero, and only significant predictors are retained at the optimal λ value